Presentation

December 9, 2024

Shirley Toribio

Diversity of Horror

Netflix Horror Movies

horror_df
  num         genre
1 125        Horror
2 110     Thrillers
3  38      Comedies
4  19 SciFi&Fantasy
5  12          Cult
6   2 Documentaties
7   2      Romantic

Netflix Horror Movies

Beta vs Normal Distribution

Function 1: PI Interval Calculation

CI <- function(data, coverage_prob){ 
  #Generates a normal prediction interval with an intended coverage probability of coverage_prob based on a vector of numeric data
  lower_zscore <- qnorm((1-coverage_prob)/2)
  upper_zscore <- qnorm(((1-coverage_prob)/2) + coverage_prob)
  avg <- mean(data)
  stan_d <- sd(data)
  lower_bound <- avg + lower_zscore*stan_d
  upper_bound <- avg + upper_zscore*stan_d
  return(data.frame(PI_percentage = coverage_prob, lower = lower_bound, upper = upper_bound))
}

Function 2: One simulation of beta-generated data

one_beta_simulation <- function(n, alpha, beta, ci_prop){
  #Assesses prediction accuracy and actual coverage probability of a normal prediction interval when used on a vector of numeric data of size n. The numeric data is generated from a beta distribution with parameters alpha and beta.
  
  cover_df <- CI(rbeta(n, alpha, beta), ci_prop)
  cover_prop <- pbeta(cover_df[1, "upper"], alpha, beta) - pbeta(cover_df[1, "lower"], alpha, beta)
  mean_in_interval <- .5 >= cover_df[1, "lower"] & .5 <= cover_df[1,"upper"]
  param_df <- data.frame(cover = cover_prop, alpha = rep(alpha, nrow(cover_df)), beta = rep(beta, nrow(cover_df)), mean_in_interval = mean_in_interval)
  df <- cbind(cover_df, param_df)
  return(df)
}

Function 3: Multiple Beta simulations

beta_sims_n <- function(n){
  #Iterates over a vector of possible alpha = beta values and applies one_beta_simulation to each possible value of alpha/beta. All simulations use data of sample size n.
  df1 <- map(parameters,\(param) one_beta_simulation(n, param, param, ci) ) %>%
  list_rbind()
  df2 <- data.frame(n = rep(n, nrow(df1)))
  df <- cbind(df2, df1)
  return(df)
}

Simulations

     n PI_percentage     lower     upper     cover alpha beta mean_in_interval
1  320          0.95 0.3222876 0.6784408 0.9545730    15   15             TRUE
2  107          0.95 0.3597021 0.6426316 0.9578534    25   25             TRUE
3  345          0.95 0.4328748 0.5650138 0.9474185   107  107             TRUE
4  354          0.95 0.4211385 0.5844857 0.9420430    67   67             TRUE
5  427          0.95 0.4429846 0.5591384 0.9539957   147  147             TRUE
6  354          0.95 0.2400498 0.7524044 0.9574436     7    7             TRUE
7  301          0.95 0.4461885 0.5571148 0.9429824   147  147             TRUE
8   24          0.95 0.3128630 0.7243206 0.9243774     9    9             TRUE
9  125          0.95 0.4278135 0.5756722 0.9667129   103  103             TRUE
10  19          0.95 0.4366048 0.5975455 0.9352990    77   77             TRUE

Results

FIN